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2d
revised Proving $ \frac{1}{c} = \frac{1}{a} + \frac{1}{b}$ in a geometric context
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2d
answered Proving $ \frac{1}{c} = \frac{1}{a} + \frac{1}{b}$ in a geometric context
2d
answered Why $-1 \leq\frac{\langle A,B\rangle}{||A||\, ||B||}\leq1$?
Apr
12
comment Set of points at which a function coincides with its convexification is compact?
Yes, I guess lower semicontinuous could work.
Apr
12
answered Set of points at which a function coincides with its convexification is compact?
Apr
12
answered $x\over(1-x)$ $y\over(1-y)$ $z\over(1-z)$ >= 8 when $x ,y ,z $ are positive proper fractions and $x+y+z = 2$
Apr
12
comment $x\over(1-x)$ $y\over(1-y)$ $z\over(1-z)$ >= 8 when $x ,y ,z $ are positive proper fractions and $x+y+z = 2$
What does proper fractions mean? Are they rational numbers?
Apr
11
comment Proving properties about matrix $A$ s.t. $A^2 = -I$
The equation you get for $\lambda$ is $\lambda^2 = -1$. This has roots $\pm i$. The sum of the eigenvalues is equal to the trace (the sum of the elements on the diagonal), and since $A$ has real entries, the trace is real.
Apr
11
answered For $n \ge 3$, every subgroup of $A_n$ with index $n$, is isomorphic to $A_{n-1}$
Apr
11
comment For $n \ge 3$, every subgroup of $A_n$ with index $n$, is isomorphic to $A_{n-1}$
I guess you could use the fact that for $n \geq 5$, normal subgroups of $S_n$ are $\{e\},A_n,S_n$. Prove that a subgroup of $A_n$ with index $n$ is a normal subgroup of a group isomorphic to $S_{n-1}$. Then its cardinality implies that it can only be $A_{n-1}$.
Apr
11
answered Proving the series doesn't converge: $\sum_{n=1}^{\infty}a_n$, $\lim_{n\to\infty}na_n=\infty$, $a_1=-1$
Apr
11
answered To find the value of a function at a point where it is continuous
Apr
11
awarded  linear-algebra
Apr
10
comment Learning modern differential geometry before curves and surfaces
I don't see why what you are doing could not be "safe". But it's just like talking about derivatives, without actually finding a derivative of a concrete function like $\exp,\sin,\ln$. Differential geometry was not a success for me, and as I look back, is this lack of concrete examples and connection with the curves and surfaces which kept me from learning more. I liked this course on curves and surfaces: alpha.math.uga.edu/~shifrin/ShifrinDiffGeo.pdf If you like differential geometry, you'll like curves and surfaces.
Apr
10
answered Proving properties about matrix $A$ s.t. $A^2 = -I$
Apr
10
comment Learning modern differential geometry before curves and surfaces
If you're comfortable with geometry on manifolds, it costs nothing to take a look into curves and surfaces. How can you speak of the tangent space to a manifold without being able to work with tangents to curves, or tangent planes to surfaces? How do you compute the curvature of a curve, or the mean curvature of a surface at a point? These are basic questions you need to know from curves and surfaces...
Apr
10
revised Equal-area sparse spherical shell partitioning
added 87 characters in body
Apr
9
comment Please help solve for the variables A and B
Replace B in the first equation. Then you'll have just an equation in A
Apr
9
comment Find all functions $f$ such that if $a+b$ is a square, then $f(a)+f(b)$ is a square
@Elaqqad: The article you cite proves this only for polynomials, as far as I see.
Apr
9
revised Unique solution of nolinear equation set
added 124 characters in body